Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=2

level: medium

position: ..1...76.6...9.4.8.....2...2..8.......7.6.5.......9..3...1.......6.4...5.15.7.9.. initial

Autosolve

position: ..1...76.6...9.4.8...6.2...2..8.......7.6.5.......9..3...1.......694...5.15.7.9.. autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # B1: 2,3 => CTR => B1: 5,8,9
* DIS # H2: 2,3 => CTR => H2: 1,5
* DIS # H3: 1,3 => CTR => H3: 5,9
* DIS # I4: 1,9 => CTR => I4: 4,6,7
* DIS # A6: 4,8 => CTR => A6: 1,5
* DIS # B6: 4,8 => CTR => B6: 5,6
* PRF # H6: 4,8 => SOL
* DIS # C7: 4,8 => CTR => C7: 2,3,9
* DIS # G6: 1,6 => CTR => G6: 2,8
* DIS # B8: 3,8 => CTR => B8: 2,7
* CNT  10 HDP CHAINS /  53 HYP OPENED
```

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

The following important HDP chains were detected:

```* DIS # B1: 2,3 => CTR => B1: 5,8,9
* DIS B1: 5,8,9 # B2: 5 => CTR => B2: 2,3
* DIS B1: 5,8,9 + B2: 2,3 # H3: 1,3 => CTR => H3: 5,9
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 # I4: 1,9 => CTR => I4: 4,6,7
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # A6: 4,8 => CTR => A6: 1,5
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 # B6: 4,8 => CTR => B6: 5,6
* PRF B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 # H6: 4,8 => SOL
* STA B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 + H6: 4,8
* CNT   7 HDP CHAINS /  13 HYP OPENED
```

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

 ..1...76.6...9.4.8.....2...2..8.......7.6.5.......9..3...1.......6.4...5.15.7.9.. initial ..1...76.6...9.4.8...6.2...2..8.......7.6.5.......9..3...1.......694...5.15.7.9.. autosolve 591483762632597418478612359259831647387264591164759283943125876726948135815376924 solved

level: medium

Pairing Analysis

```--------------------------------------------------
* PAIRS (8)
C2: 2,3
I1: 2,9
G3: 1,3
I3: 1,9
C6: 4,8
G4: 1,6
F8: 3,8
D9: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F2,E3: 1.. / F2 = 1  =>  9 pairs (_) / E3 = 1  =>  0 pairs (*)
A5,A6: 1.. / A5 = 1  => 11 pairs (_) / A6 = 1  => 17 pairs (_)
G8,H8: 1.. / G8 = 1  =>  8 pairs (_) / H8 = 1  => 10 pairs (_)
F2,H2: 1.. / F2 = 1  =>  9 pairs (_) / H2 = 1  =>  0 pairs (*)
I1,H2: 2.. / I1 = 2  =>  8 pairs (_) / H2 = 2  =>  0 pairs (X)
E7,D9: 2.. / E7 = 2  =>  0 pairs (*) / D9 = 2  =>  0 pairs (X)
B1,I1: 2.. / B1 = 2  =>  0 pairs (X) / I1 = 2  =>  8 pairs (_)
C2,C7: 2.. / C2 = 2  =>  8 pairs (_) / C7 = 2  =>  0 pairs (X)
E6,E7: 2.. / E6 = 2  =>  9 pairs (_) / E7 = 2  =>  0 pairs (*)
D1,F1: 4.. / D1 = 4  => 13 pairs (_) / F1 = 4  => 10 pairs (_)
H2,H3: 5.. / H2 = 5  => 15 pairs (_) / H3 = 5  =>  8 pairs (_)
E7,F7: 5.. / E7 = 5  => 15 pairs (_) / F7 = 5  => 11 pairs (_)
B4,B6: 6.. / B4 = 6  =>  0 pairs (X) / B6 = 6  =>  8 pairs (_)
F7,F9: 6.. / F7 = 6  => 17 pairs (_) / F9 = 6  => 11 pairs (_)
B6,G6: 6.. / B6 = 6  =>  8 pairs (_) / G6 = 6  =>  0 pairs (X)
F9,I9: 6.. / F9 = 6  => 11 pairs (_) / I9 = 6  => 17 pairs (_)
A3,B3: 7.. / A3 = 7  => 11 pairs (_) / B3 = 7  =>  8 pairs (_)
D2,F2: 7.. / D2 = 7  =>  8 pairs (_) / F2 = 7  =>  0 pairs (*)
F4,D6: 7.. / F4 = 7  =>  8 pairs (_) / D6 = 7  =>  0 pairs (*)
D6,H6: 7.. / D6 = 7  =>  0 pairs (*) / H6 = 7  =>  0 pairs (X)
D2,D6: 7.. / D2 = 7  =>  8 pairs (_) / D6 = 7  =>  0 pairs (*)
F2,F4: 7.. / F2 = 7  =>  0 pairs (*) / F4 = 7  =>  0 pairs (X)
I4,I7: 7.. / I4 = 7  =>  0 pairs (*) / I7 = 7  =>  0 pairs (X)
* DURATION: 0:00:30.829756  START: 03:21:44.829963  END: 03:22:15.659719 2017-05-01
* CP COUNT: (23)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C6,D9,F8,G3,G4,I1,I3)
* ..1...76.6...9.4.8...6.2...2..8.......7.6.5.......9..3...1.......694...5.15.7.9..
* PAIR C2: 2,3 BLK 1
B1: 2,3,5,8,9                            # reduction candidate for 2,3
B1: 2,3 => CTR
* .21534769653791428...68235123.857..61.7.635..56..19.73..21.5.....6948..5.15.769..
B1: 5,8,9                                #  8 pairs
B2: 2,3,5                                # reduction candidate for 2,3
B2: 2,3                                  # 13 pairs
* PAIR C2: 2,3 ROW 2
H2: 2,3,1,5                              # reduction candidate for 2,3
H2: 2,3 => CTR
* ..15.4762652791438.7.6.215.2..857.....7.6.5..5...19.73...1256.7.2694...5.153769..
H2: 1,5                                  # 11 pairs
* PAIR C2: 2,3 COL C
C7: 2,3,4,8,9                            # reduction candidate for 2,3
C7: 2,3                                  # 10 pairs
C7: 4,8,9                                #  8 pairs
* PAIR I1: 2,9 ROW 1
B1: 2,9,3,5,8                            # reduction candidate for 2,9
B1: 2,9                                  #  9 pairs
B1: 3,5,8                                #  8 pairs
* PAIR I1: 2,9 COL I
I5: 2,9,1,4                              # reduction candidate for 2,9
I5: 2,9                                  # 13 pairs
I5: 1,4                                  #  9 pairs
* PAIR G3: 1,3 BLK 3
H2: 1,3,2,5                              # reduction candidate for 1,3
H2: 1,3                                  #  9 pairs
H3: 1,3,5,9                              # reduction candidate for 1,3
H3: 1,3 => CTR
* ..1..57626..791458...682..92..8.76....7.645.1164..9.73...1.6..7..694...5.15.7.9.6
H3: 5,9                                  #  9 pairs
* PAIR G3: 1,3 ROW 3
E3: 1,3,5,8                              # reduction candidate for 1,3
E3: 1,3                                  # 12 pairs
E3: 5,8                                  # 10 pairs
* PAIR G3: 1,3 COL G
G8: 1,3,2,8                              # reduction candidate for 1,3
G8: 2,8                                  # 11 pairs
G8: 1,3                                  # 10 pairs
* PAIR I3: 1,9 BLK 3
H3: 1,9,3,5                              # reduction candidate for 1,9
H3: 1,9                                  # 15 pairs
H3: 3,5                                  #  9 pairs
* PAIR I3: 1,9 COL I
I4: 1,9,4,6,7                            # reduction candidate for 1,9
I4: 1,9 => CTR
* ..1...7626...9.4.8...6.2...2..8.......73615.4.....9..3...156..7..694...5.1527.9.6
I4: 4,6,7                                #  8 pairs
I5: 1,9,2,4                              # reduction candidate for 1,9
I5: 1,9                                  #  9 pairs
* PAIR C6: 4,8 BLK 4
A5: 4,8,1,3,9                            # reduction candidate for 4,8
A5: 4,8                                  # 20 pairs
B5: 4,8,3,9                              # reduction candidate for 4,8
B5: 4,8                                  # 12 pairs
A6: 4,8,1,5                              # reduction candidate for 4,8
A6: 4,8 => CTR
* ..1...7626...9.4.8...6.2...2..8.....1.7264589.....9..3...125....2694...5.15376924
A6: 1,5                                  #  9 pairs
B6: 4,8,5,6                              # reduction candidate for 4,8
B6: 4,8 => CTR
* ..1...76.6...9.4.8...6.2...26.8..1....7.6.5..5...196.3...125..6.2694..15.153769..
B6: 5,6                                  #  9 pairs
* PAIR C6: 4,8 ROW 6
H6: 4,8,1,2,7                            # reduction candidate for 4,8
H6: 4,8 => SOLVED
* 591483762632597418478612359259831647387264591164759283943125876726948135815376924
H6: 1,2,7                                #  8 pairs
* PAIR C6: 4,8 COL C
C3: 4,8,3,9                              # reduction candidate for 4,8
C3: 4,8                                  # 10 pairs
C7: 4,8,2,3,9                            # reduction candidate for 4,8
C7: 4,8 => CTR
* ..1...762652.91438..36.21592.98.7641..7.6.59..6...9..3...1.......694..15.15.7.9..
C7: 2,3,9                                #  8 pairs
* PAIR G4: 1,6 BLK 6
I4: 1,6,4,7,9                            # reduction candidate for 1,6
I4: 1,6                                  # 11 pairs
G6: 1,6,2,8                              # reduction candidate for 1,6
G6: 1,6 => CTR
* ..1...76.6..7914.8...6.23.12538176..197.6.582.6.529173...1.6..7..694..15.1527.9.6
G6: 2,8                                  #  9 pairs
* PAIR F8: 3,8 BLK 8
E7: 3,8,2,5                              # reduction candidate for 3,8
E7: 3,8                                  # 13 pairs
F7: 3,8,5,6                              # reduction candidate for 3,8
F7: 3,8                                  # 19 pairs
F9: 3,8,6                                # reduction candidate for 3,8
F9: 3,8                                  # 17 pairs
* PAIR F8: 3,8 ROW 8
A8: 3,8,7                                # reduction candidate for 3,8
A8: 3,8                                  # 11 pairs
B8: 3,8,2,7                              # reduction candidate for 3,8
B8: 3,8 => CTR
* ..1..576.6.2791458574682...2538176....7.6452.468529.73...1.6..77.694.215.1527.9.6
B8: 2,7                                  #  9 pairs
G8: 3,8,1,2                              # reduction candidate for 3,8
G8: 3,8                                  # 14 pairs
H8: 3,8,1,2,7                            # reduction candidate for 3,8
H8: 3,8                                  # 13 pairs
* PAIR F8: 3,8 COL F
F1: 3,8,4,5                              # reduction candidate for 3,8
F1: 3,8                                  # 17 pairs
F1: 4,5                                  #  9 pairs
* PAIR D9: 2,3 BLK 8
E7: 2,3,5,8                              # reduction candidate for 2,3
E7: 2,3                                  # 13 pairs
E7: 5,8                                  # 11 pairs
* PAIR D9: 2,3 ROW 9
H9: 2,3,4,8                              # reduction candidate for 2,3
H9: 2,3                                  # 12 pairs
H9: 4,8                                  #  9 pairs
* PAIR D9: 2,3 COL D
D5: 2,3,4                                # reduction candidate for 2,3
D5: 4                                    # 13 pairs
D5: 2,3                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0002-base-pr-000.dot
* REASONING
* DIS # B1: 2,3 => CTR => B1: 5,8,9
* DIS # H2: 2,3 => CTR => H2: 1,5
* DIS # H3: 1,3 => CTR => H3: 5,9
* DIS # I4: 1,9 => CTR => I4: 4,6,7
* DIS # A6: 4,8 => CTR => A6: 1,5
* DIS # B6: 4,8 => CTR => B6: 5,6
* PRF # H6: 4,8 => SOL
* DIS # C7: 4,8 => CTR => C7: 2,3,9
* DIS # G6: 1,6 => CTR => G6: 2,8
* DIS # B8: 3,8 => CTR => B8: 2,7
* CNT  10 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C6,D9,F8,G3,G4,I1,I3)
* ..1...76.6...9.4.8...6.2...2..8.......7.6.5.......9..3...1.......694...5.15.7.9..
* PAIR C2: 2,3 BLK 1
B1: 2,3,5,8,9                            # reduction candidate for 2,3
B1: 2,3 => CTR
* .21534769653791428...68235123.857..61.7.635..56..19.73..21.5.....6948..5.15.769..
B2: 2,3,5                                # reduction candidate for 2,3
B2: 2,3                                  # 13 pairs
* RESTART
* PAIR C2: 2,3 BLK 1
B2: 2,3,5                                # reduction candidate for 2,3
B2: 5 => CTR
* ..15.4762652.9.4.8...6.2.592..8.....1.7.635.45..4.9.73...1....7..6948..5.15.769..
* PAIR C2: 2,3 COL C
C7: 2,3,9                                # reduction candidate for 2,3
C7: 2,3                                  # 13 pairs
C7: 9                                    # 11 pairs
* PAIR G3: 1,3 BLK 3
H3: 1,3,5,9                              # reduction candidate for 1,3
H3: 1,3 => CTR
* ..1..57626..791458...682..92..8.76....7.645.116...9.73...1.6..7..694...5.15.7.9.6
* PAIR I3: 1,9 COL I
I4: 1,9,4,6,7                            # reduction candidate for 1,9
I4: 1,9 => CTR
* ..1...7626...9.4.8...6.23..2..8.......73615.4.....9..3...156..7..694...5.1527.9.6
* RESTART
* PAIR RESTART
* PAIR C6: 4,8 BLK 4
A5: 4,8,1,3,9                            # reduction candidate for 4,8
A5: 4,8                                  # 21 pairs
B5: 4,8,3,9                              # reduction candidate for 4,8
B5: 4,8                                  # 17 pairs
A6: 4,8,1,5                              # reduction candidate for 4,8
A6: 4,8 => CTR
* ..1...7626.3791458...6.23912.9837...137.64589.6..19273..21....7..694..25.1527.9..
B6: 4,8,5,6                              # reduction candidate for 4,8
B6: 4,8 => CTR
* ..1...7626...9.4.8...6.23..26.8..1....7.6.5.95...196.3...1258.6.2694...5.15.7.9..
* PAIR C6: 4,8 ROW 6
H6: 4,8,1,2,7                            # reduction candidate for 4,8
H6: 4,8 => SOLVED
* 591483762632597418478612359259831647387264591164759283943125876726948135815376924
* DURATION: 0:00:13.639782  START: 03:22:48.996415  END: 03:23:02.636197 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0002-base-pr-001.dot
* REASONING
* DIS # B1: 2,3 => CTR => B1: 5,8,9
* DIS B1: 5,8,9 # B2: 5 => CTR => B2: 2,3
* DIS B1: 5,8,9 + B2: 2,3 # H3: 1,3 => CTR => H3: 5,9
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 # I4: 1,9 => CTR => I4: 4,6,7
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # A6: 4,8 => CTR => A6: 1,5
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 # B6: 4,8 => CTR => B6: 5,6
* PRF B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 # H6: 4,8 => SOL
* STA B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 + H6: 4,8
* CNT   7 HDP CHAINS /  13 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=2
```

Solution

position: 591483762632597418478612359259831647387264591164759283943125876726948135815376924 solved

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

```* DIS # B1: 2,3 => CTR => B1: 5,8,9
* INC # B1: 5,8,9 => UNS
* INC # B2: 2,3 => UNS
* DIS # H2: 2,3 => CTR => H2: 1,5
* INC # H2: 1,5 => UNS
* INC # C7: 2,3 => UNS
* INC # C7: 4,8,9 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 3,5,8 => UNS
* INC # I5: 2,9 => UNS
* INC # I5: 1,4 => UNS
* INC # H2: 1,3 => UNS
* DIS # H3: 1,3 => CTR => H3: 5,9
* INC # H3: 5,9 => UNS
* INC # E3: 1,3 => UNS
* INC # E3: 5,8 => UNS
* INC # G8: 1,3 => UNS
* INC # G8: 2,8 => UNS
* INC # H3: 1,9 => UNS
* INC # H3: 3,5 => UNS
* DIS # I4: 1,9 => CTR => I4: 4,6,7
* INC # I4: 4,6,7 => UNS
* INC # I5: 1,9 => UNS
* INC # A5: 4,8 => UNS
* INC # B5: 4,8 => UNS
* DIS # A6: 4,8 => CTR => A6: 1,5
* INC # A6: 1,5 => UNS
* DIS # B6: 4,8 => CTR => B6: 5,6
* INC # B6: 5,6 => UNS
* PRF # H6: 4,8 => SOL
* INC # H6: 1,2,7 => UNS
* INC # C3: 4,8 => UNS
* DIS # C7: 4,8 => CTR => C7: 2,3,9
* INC # C7: 2,3,9 => UNS
* INC # I4: 1,6 => UNS
* DIS # G6: 1,6 => CTR => G6: 2,8
* INC # G6: 2,8 => UNS
* INC # E7: 3,8 => UNS
* INC # F7: 3,8 => UNS
* INC # F9: 3,8 => UNS
* INC # A8: 3,8 => UNS
* DIS # B8: 3,8 => CTR => B8: 2,7
* INC # B8: 2,7 => UNS
* INC # G8: 3,8 => UNS
* INC # H8: 3,8 => UNS
* INC # F1: 3,8 => UNS
* INC # F1: 4,5 => UNS
* INC # E7: 2,3 => UNS
* INC # E7: 5,8 => UNS
* INC # H9: 2,3 => UNS
* INC # H9: 4,8 => UNS
* INC # D5: 2,3 => UNS
* INC # D5: 4 => UNS
* CNT  53 HDP CHAINS /  53 HYP OPENED
```

A2. Pair Reduction

Full list of HDP chains traversed:

```* DIS # B1: 2,3 => CTR => B1: 5,8,9
* INC B1: 5,8,9 # B2: 2,3 => UNS
* INC B1: 5,8,9 # B2: 2,3 => UNS
* DIS B1: 5,8,9 # B2: 5 => CTR => B2: 2,3
* INC B1: 5,8,9 + B2: 2,3 # C7: 2,3 => UNS
* INC B1: 5,8,9 + B2: 2,3 # C7: 9 => UNS
* DIS B1: 5,8,9 + B2: 2,3 # H3: 1,3 => CTR => H3: 5,9
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 # I4: 1,9 => CTR => I4: 4,6,7
* INC B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # A5: 4,8 => UNS
* INC B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # B5: 4,8 => UNS
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 # A6: 4,8 => CTR => A6: 1,5
* DIS B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 # B6: 4,8 => CTR => B6: 5,6
* PRF B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 # H6: 4,8 => SOL
* STA B1: 5,8,9 + B2: 2,3 + H3: 5,9 + I4: 4,6,7 + A6: 1,5 + B6: 5,6 + H6: 4,8
* CNT  13 HDP CHAINS /  13 HYP OPENED
```